Aircraft: MD-11
Phase of flight: Climb
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy

We were issued a clearance thru ACARS 'RWY 27L VIA OPALE 3A...' As PF I loaded Runway 27L and the OPALE 3A departure into the FMS. I verified the waypoints in the FMS comparing the data to the OPALE 3A SID chart. I also verified the waypoints against the Dispatch Release just as an additional back-up. I then briefed the ACARS CLNC with the First Officer and finally did a complete briefing of the departure procedure reading from the FMS while the First Officer verified all fixes and data looking at the chart. At no time was any error noted at all. After engine start I engaged NAV and verified the FCP was still in NAV Mode in conjunction with the Before Takeoff Checklist once cleared onto the runway for takeoff. When LFPG Tower cleared us for takeoff on 27L they asked to verify that we had loaded the OPALE 3A departure. I looked at the FMS and saw - again - that the OPALE 3A was in fact loaded in the FMS and the First Officer acknowledged this fact. Takeoff was normal - NADP 1 using NAV MODE from the start of takeoff. As I approached PG270 (the first fix) I selected IAS HOLD so as to achieve a better turn radius for the turn at that fix; staying around 180 KIAS. After switching to Departure Control; the Controller told us to climb to FL140 (I think) and asked us to expedite thru FL120. Once past PG270 and as we were approaching PG276 (the next waypoint) the Controller asked us again to verify the departure we were flying. I again looked at the FMS and verified that we were still on the OPALE 3A and re-verified that I was in NAV. At this point the Controller told us that we were 1.5 miles from our course! He quoted a radial that we weren't tracking and we advised him of the waypoints we were using for the RNAV departure (again exactly what the OPALE 3A called for). At NO TIME were we more that .2 miles from the magenta line according to our data tag on the NAV Display and at no time were we not in NAV during the entire departure phase. The Controller did not seem upset but he was adamant that we were well off course and suggested that perhaps we were not properly navigating and/or that our speed was too fast. This discrepancy is really a mystery. My First Officer and I reviewed everything again once we were in cruise and just simply can't come up with an explanation other that the Controller was wrong or;(much less likely) that the chart and FMS database are not correct. We were cleared for takeoff on Runway 27L. We were cleared on the OPALE 1A [3A]. Not only did the Captain put in the check point from the release; but we checked the way points per SOP. When the [clearance] came over the ACARS; we then checked the points again on the departure. We were cleared for takeoff on Runway 27L. Just before we switched to Departure; DeGualle Tower reminded us we were on the OPALE 1A [3A] departure. I thought to myself that was a strange time to 'remind' us of the departure. I read back the clearance and switched frequency. We switched to departure and we were told to expedite through FL120. The Captain did a speed hold of around 170-180 KIAS and kept the slats out. When we made our first turn on the SID (just past PH276) [PG270] DeGualle Departure came on and told us we were 1.5 miles off course. I looked at my display and it showed L 0.1 which is normal on the turn. When we said we were showing on course; DeGualle came back and started reading the radials of the CGN [BT] VOR that we 'missed'. We reminded DeGualle that we were on the RNAV departure. Again the speed was quite slow so there is no way we were off course. The airplane was on the magenta line. The Captain then jumped on the radio. He read the SID directly to departure and read each way point to them on the frequency 'OPALE 1A [3A] Departure; PH276 [PG276]; Beauvais (BVS); OPALE.' It is a very simple departure. We were NEVER off course. As soon as the Captain read the points back; departure said it was for our 'information' only and no problem. They were never upset and acted like it was no big deal - only for our information. They also said it looks as if we were 'now correcting back on course'. I was like; what? We were still on the magenta line and never off nor were we trying to correct?? That's when I really started thinking they were screwing up. We were not correcting - we were never off course. I have to admit that this was one of the weirdest things I have ever been involved in. A minute or two later DeGualle said we were on course and call London Control. I am 100% confident that we were never off course unless the FMS database was incorrect. MD11 flight crew departing LFPG on the Oaple 3A RNAV departure is informed by ATC that they are off course. The crew can detect no errors and their map display shows they are on course.